# Mathematical Foundation and Corrections for Full Range Head Pose Estimation

arXiv: https://arxiv.org/abs/2403.18104 · HTML: https://mlsanity.com/paper/2403.18104/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 35 references that are in the map.
- First posted on arXiv 26 Mar 2024.

## Builds on (most cited first, 14 of 14)

- [Expressive Body Capture: 3D Hands, Face, and Body from a Single Image](https://mlsanity.com/paper/1904.05866/) (2019)
- [OpenPose: Realtime Multi-Person 2D Pose Estimation using Part Affinity Fields](https://mlsanity.com/paper/1812.08008/) (2018)
- [RepVGG: Making VGG-style ConvNets Great Again](https://mlsanity.com/paper/2101.03697/) (2021)
- [Hand Keypoint Detection in Single Images using Multiview Bootstrapping](https://mlsanity.com/paper/1704.07809/) (2017)
- [Towards Fast, Accurate and Stable 3D Dense Face Alignment](https://mlsanity.com/paper/2009.09960/) (2020)
- [AGORA: Avatars in Geography Optimized for Regression Analysis](https://mlsanity.com/paper/2104.14643/) (2021)
- [Panoptic Studio: A Massively Multiview System for Social Interaction Capture](https://mlsanity.com/paper/1612.03153/) (2016)
- [Fine-Grained Head Pose Estimation Without Keypoints](https://mlsanity.com/paper/1710.00925/) (2017)
- [Face Alignment in Full Pose Range: A 3D Total Solution](https://mlsanity.com/paper/1804.01005/) (2018)
- [6D Rotation Representation For Unconstrained Head Pose Estimation](https://mlsanity.com/paper/2202.12555/) (2022)
- [WHENet: Real-time Fine-Grained Estimation for Wide Range Head Pose](https://mlsanity.com/paper/2005.10353/) (2020)
- [FaceBoxes: A CPU Real-time Face Detector with High Accuracy](https://mlsanity.com/paper/1708.05234/) (2017)
- [A Vector-based Representation to Enhance Head Pose Estimation](https://mlsanity.com/paper/2010.07184/) (2020)
- [DirectMHP: Direct 2D Multi-Person Head Pose Estimation with Full-range Angles](https://mlsanity.com/paper/2302.01110/) (2023)

## Built on by (most cited first, 3 of 3)

- [HPE-CogVLM: Advancing Vision Language Models with a Head Pose Grounding Task](https://mlsanity.com/paper/2406.01914/) (2024)
- [Full-range Head Pose Geometric Data Augmentations](https://mlsanity.com/paper/2408.01566/) (2024)
- [CLERF: Contrastive LEaRning for Full Range Head Pose Estimation](https://mlsanity.com/paper/2412.02066/) (2024)

## Abstract (arXiv)

Numerous works concerning head pose estimation (HPE) offer algorithms or proposed neural network-based approaches for extracting Euler angles from either facial key points or directly from images of the head region. However, many works failed to provide clear definitions of the coordinate systems and Euler or Tait-Bryan angles orders in use. It is a well-known fact that rotation matrices depend on coordinate systems, and yaw, roll, and pitch angles are sensitive to their application order. Without precise definitions, it becomes challenging to validate the correctness of the output head pose and drawing routines employed in prior works. In this paper, we thoroughly examined the Euler angles defined in the 300W-LP dataset, head pose estimation such as 3DDFA-v2, 6D-RepNet, WHENet, etc, and the validity of their drawing routines of the Euler angles. When necessary, we infer their coordinate system and sequence of yaw, roll, pitch from provided code. This paper presents (1) code and algorithms for inferring coordinate system from provided source code, code for Euler angle application order and extracting precise rotation matrices and the Euler angles, (2) code and algorithms for converting poses from one rotation system to another, (3) novel formulae for 2D augmentations of the rotation matrices, and (4) derivations and code for the correct drawing routines for rotation matrices and poses. This paper also addresses the feasibility of defining rotations with right-handed coordinate system in Wikipedia and SciPy, which makes the Euler angle extraction much easier for full-range head pose research.